Skip to main content
SpringerLink
Log in

Fuzzy Hypergraphs

  • Chapter
  • First Online:
Fuzzy Hypergraphs and Related Extensions

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 390))

Abstract

In this chapter, we present fundamental and technical concepts like fuzzy hypergraphs, fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy k-competition hypergraphs, fuzzy neighborhood hypergraphs, and \({\mathscr {N}}\)-hypergraphs. We describe applications of fuzzy competition hypergraphs in decision support systems, including predator–prey relations in ecological niches, social networks, and business marketing. Further, we introduce complex fuzzy hypergraphs, \(\mu e^{i\theta }\)-level hypergraphs, covering constructions, 2-sections, and \(L_2\)-sections of these hypergraphs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abdul-Jabbar, N., Naoom, J.H., Ouda, E.H.: Fuzzy dual graph. J. Al-Nahrain Univ. 12(4), 168–171 (2009)

    Google Scholar 

  2. Akram, M.: Studies in Fuzziness and Soft Computing. Fuzzy Lie algebras, vol. 9, pp. 1–302. Springer, Berlin (2018)

    Google Scholar 

  3. Akram, M., Alshehri, N.O.: Tempered interval-valued fuzzy hypergraphs. Sci. Bull. Ser. A Appl. Math. Phys. 77(1), 39–48 (2015)

    MathSciNet  MATH  Google Scholar 

  4. Akram, M., Chen, W.J., Davvaz, B.: On \({\cal{N}}\)-hypergraphs. J. Intell. Fuzzy Syst. 26, 2937–2944 (2014)

    Article  Google Scholar 

  5. Berge, C.: Graphs and Hypergraphs. North-Holland, Amsterdam (1973)

    MATH  Google Scholar 

  6. Craine, M.W.L.: Fuzzy hypergraphs and fuzzy intersection graphs. University of Idaho, Ph.D Thesis (1993)

    Google Scholar 

  7. Goetschel Jr., R.H.: Introduction to fuzzy hypergraphs and Hebbian structures. Fuzzy Sets Syst. 76, 113–130 (1995)

    Article  MathSciNet  Google Scholar 

  8. Goetschel Jr., R.H.: Fuzzy colorings of fuzzy hypergraphs. Fuzzy Sets Syst. 94, 185–204 (1998)

    Article  MathSciNet  Google Scholar 

  9. Goetschel Jr., R.H., Craine, W.L., Voxman, W.: Fuzzy transversals of fuzzy hypergraphs. Fuzzy Sets Syst. 84, 235–254 (1996)

    Article  MathSciNet  Google Scholar 

  10. Jun, Y.B., Lee, K.J., Song, S.Z.: \({\cal{N}}\)-ideals of \(BCK/BCI\)-algebras. J. Chungcheong Math. Soc. 22, 417–437 (2009)

    Google Scholar 

  11. Kaufmann, A.: Introduction a la Thiorie des Sous-Ensemble Flous, 1. Masson, Paris (1977)

    Google Scholar 

  12. Lee-kwang, H., Lee, K.-M.: Fuzzy hypergraph and fuzzy partition. IEEE Trans. Syst. Man Cybern. 25(1), 196–201 (1995)

    Article  MathSciNet  Google Scholar 

  13. Lung, R.I., Gasko, N., Suciu, M.A.: A hypergraph model for representing scientific output. Scientometrics 117(3), 1361–1379 (2018)

    Article  Google Scholar 

  14. Mendel, J.M.: Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Upper Saddle River, New Jersey (2001)

    MATH  Google Scholar 

  15. Mordeson, J.N., Chang-Shyh, P.: Operations on fuzzy graphs. Inf. Sci. 79, 159–170 (1994)

    Article  MathSciNet  Google Scholar 

  16. Mordeson, J.N.: Fuzzy line graph. Pattern Recognit. Lett. 14, 381–384 (1993)

    Article  Google Scholar 

  17. Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, 2nd edn. Physica Verlag, Heidelberg (2001)

    MATH  Google Scholar 

  18. Mordeson, J.N., Yao, Y.Y.: Fuzzy cycles and fuzzy trees. J. Fuzzy Math. 10, 189–202 (2002)

    MathSciNet  MATH  Google Scholar 

  19. Radhamani, C., Radhika, C.: Isomorphism on fuzzy hypergraphs. IOSR J. Math. 2(6), 24–31 (2012)

    Google Scholar 

  20. Radhika, C., Radhamani, C., Suresh, S.: Isomorphism properties on strong fuzzy hypergraphs. Int. J. Comput. Appl. 64(1)(2013)

    Article  Google Scholar 

  21. Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)

    Article  Google Scholar 

  22. Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and their Applications, pp. 77–95. Academic Press, New York (1975)

    Google Scholar 

  23. Samanta, S., Akram, M., Pal, M.: \(m\)-Step fuzzy competition graphs. J. Appl. Math. Comput. 47, 461–472 (2015)

    Article  MathSciNet  Google Scholar 

  24. Samanta, S., Pal, M.: Fuzzy \(k\)-competition graphs and \(p\)-competition fuzzy graphs. Fuzzy Inf. Eng. 5, 191–204 (2013)

    Article  MathSciNet  Google Scholar 

  25. Sarwar, M., Akram, M., Alshehri, N.O.: A new method to decision-making with fuzzy competition hypergraphs. Symmetry 10(9), 404 (2018). https://doi.org/10.3390/sym10090404

    Article  Google Scholar 

  26. Sonntag, M., Teichert, H.M.: Competition hypergraphs. Discr. Appl. Math. 143, 324–329 (2004)

    Article  MathSciNet  Google Scholar 

  27. Sonntag, M., Teichert, H.M.: Competition hypergraphs of digraphs with certain properties II, Hamiltonicity. Discuss. Math. Graph Theory 28, 23–34 (2008)

    Article  MathSciNet  Google Scholar 

  28. Thirunavukarasu, P., Suresh, R., Viswanathan, K.K.: Energy of a complex fuzzy graph. Int. J. Math. Sci. Eng. Appl. 10(1), 243–248 (2016)

    Google Scholar 

  29. Yazdanbakhsh, O., Dick, S.: A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst. 338, 1–22 (2018)

    Article  MathSciNet  Google Scholar 

  30. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

  31. Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)

    Article  MathSciNet  Google Scholar 

  32. Zadeh, L.A.: The concept of a linguistic and application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Lahore, Pakistan

    Muhammad Akram

  2. Department of Mathematics, University of the Punjab, Lahore, Pakistan

    Anam Luqman

Authors
  1. Muhammad Akram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anam Luqman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Akram .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Akram, M., Luqman, A. (2020). Fuzzy Hypergraphs. In: Fuzzy Hypergraphs and Related Extensions. Studies in Fuzziness and Soft Computing, vol 390. Springer, Singapore. https://doi.org/10.1007/978-981-15-2403-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-981-15-2403-5_1

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-2402-8

  • Online ISBN: 978-981-15-2403-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation